Me to Geekman: "I'm always slightly concerned when the grades for an assignment form a perfect bell-curve."
Geekman: "Why?"
Me: "Because they never have before! (So maybe "always" wasn't the right word.) And it makes me worry I have set an assignment that tests intelligence rather than what they should have been learning."
Geekman, cryptically: "A convolution of two Gaussians is still Gaussian."
Me: "Two? What's the other one?"
Geekman: "I mean, if they are normally distributed for intelligence, and for hard-workingness, then you will still get a normal distribution."
Me: "But I don't think their success or failure in the assignment should depend on intelligence and hard-workingness."
Geekman: "What should it depend on?"
Me: "Whether or not they learned the material. And it's not hard, so they bloody well should have. Which means they should all get 100%... except for the ones who didn't come to class. They should get zero."
Geekman: "And then there's the morons. There will always be some morons."
Me: "Okay, so I want a trinominal distribution. A lump of absentees together near the bottom; a blob of morons in the middle; and everyone else together at the top. Do you think I can scale for that?"
(Posted here instead of at the secret hiding place, because I've run out of non-teaching-related material for here.)
Tuesday, September 11, 2007
Styleygeek understands statistics
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6 Comments:
I'm sorry, but you'll have no such luck. There's always one Chad in the bunch.
[mutters]Them darn Chads.
I think there's a reference I'm not getting :( Who's Chad?
Um, but doesn't intelligence or hard-workingness have anything to do with whether they learned the material??
Yes, but not in a way that I would have expected to equate to a bell curve. I feel that if they are smart enough to get in to university, even the ones on the bottom of the bell should be smart enough to understand the material from a first year course: if they aren't, then there's a fault either in admissions, or in my teaching. As for hardworkingness, if the assignment should take, say 10 hours of work, then anyone who works harder than that shouldn't necessarily do better than someone who just spends the 10 hours. So you shouldn't get a bell-curve there, either.
Chad is a sketch of a little bloke hanging onto the top of a brick wall, with just the top of his head, nose and eyes and hands visible. Very common WW2 graffito, often with a slogan written on the brick wall bit of the sketch, usually a complaint about wartime shortages (usual form 'Wot! No Bananas?', etc) or sometimes the use of the phrase 'Kilroy was here', which itself is borrowed from a US railways Rolling Stock inspector, who used to sign the above on all merchandise that passed through his railyard in the '30s and 40's to signify that he'd inspected it, and it took on a life of it's own.
I like Chad, he's cute
My brain is full of useful info like that.
When I did the unit on testing (which I hated) for my masters, I remember learning that bell curves are WRONG for testing at the end of a course. If you test at the beginning of a course, a bell curve is fine, but at the end it should be pushed up to the right, showing that the material has been learned (and taught), and that the test was an good one (i.e. did not include material that was not taught, or trick questions, or bad questions).
But I have also learned that administrators hate lopsided curves. They prefer bell curves.
Writing good tests is HARD. Luckily the ones I write are never important.
Talk to me! (You know you want to!)